He was in danger of being drawn into a lengthy battle in an edgy second set, but came through in the tie-break and wrapped things up after two hours and 37 minutes.
A straightforward afternoon seemed to be unfolding when Murray played a terrific game that included a deft half-volley, a deadly backhand lob and a brilliant forehand pass, to lead by a set and a break.
What followed was distinctly unimpressive, however, with his second serve coming under attack from the Russian 20th seed.
Match time: 2 hrs 17 mins
1st serve %
1st serve win %
2nd serve win %
When Murray double-faulted to drop serve for the second game in succession and then fell 5-2 behind, he was under real pressure for the first time in the tournament.
Youzhny, playing in the last 16 at Wimbledon for the eighth time, had his chance to level when he served for the set, but after seeing off two break-back points he could do nothing about a Murray forehand on the third.
The Scot was still searching for consistency, and another double-fault saw him change ends 4-2 down in the tie-break, but the most delicate of drop shots shifted the momentum.
Murray cracked a cross-court backhand winner on set point and, after Youzhny received treatment on his shoulder, the third set was a one-sided affair.
The Russian tamely handed over his serve in the second game and Murray broke for the fifth time before sealing victory with a blistering forehand and a serve-volley.
"It was a tough match, the first couple of sets especially, but once I got ahead in the third I concentrated hard on not letting him back in like I did in the second set," Murray told BBC Sport.
Tim HenmanFormer British number one and BBC Sport expert
"It was not Murray's best performance but in a Grand Slam you are not always going to be at your best but he has beaten a good grass court player. It was an average performance but he can go away and work on some of those things that didn't work."
"I don't take anything for granted. I know how hard these tournaments are to win. There are no guarantees here and I don't come into them thinking I am going to win.
"I just concentrate on each game. Serena lost today; Roger [Federer] has lost and Rafa [Nadal] has lost, so you cannot take anything for granted."
"There's no cause for concern. My back is what it is. It's felt way, way better than it was a few weeks ago," he added.
"There's a few times on the court where you feel things. You just have to find a way of managing those issues and getting through them because a lot of guys have had problems during this Slam especially.
"A lot of guys have had trainers on court and whatnot. So everyone's got little niggles. You just have to manage them and get through it."
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